Question

Company A considers acquiring company B. Shares of the company A trade at $30 and there are 5,000 of A shares outstanding. Company B has 200 shares outstanding worth $100 each. If A acquires B, then the resulting synergy will amount to $10,000.

Suppose A offers to exchange every B’s share for four shares in the merged company.

1.What will be the share price of the merged company?

2. What will be the total benefit for the existing shareholders of A?

3. What will be the total benefit for the existing shareholders of B?

4.  Suppose A offers to exchange every B’s share for $130 in cash. What will be the share price of the merged company?

5.  Suppose A offers to exchange every B’s share for $130 in cash. What will be the total benefit for the existing shareholders of A?

6. Suppose A offers to exchange every B’s share for $130 in cash. What will be the total benefit for the existing shareholders of B?

Answer 1

Solution:

1.

The formula to calculate the share price of the merged company is as follows:

MPSA+B = {(MPS of A * Number of shares outstanding of A) + (MPS of B * Number of shares outstanding of B) + Synergy} / {Number of shares outstanding of A + (Number of shares outstanding of B * Exchange ratio)}

              = {($30 * 5,000) + ($100 * 200) + $10,000} / {5,000 + (200 * 4)}

            = ($150,000 + $20,000 + $10,000) / 5,000 + 800

            = $180,000 / 5,800

            = $31.034

Hence, the share price of the company after merger is $31.034.

2.

The formula to calculate the total benefit to the shareholders of A is as follows:

Benefit after merger = (MPS after merger * Number of shares of A) – (MPS of A before merger * Number of shares of A)

                                  = ($31.034 * 5,000 – $30 * 5,000)

                                  = $155,170 - $150,000

                                 = $5,170

Hence, the total benefit to the shareholders of the A is $5,170.

3.

The formula to calculate the total benefit to the shareholders of the B is as follows:

Benefit after merger = {MPS after merger * (Exchange ratio * Number of shares of B)} – (MPS of B before merger * Number of shares of B)

                                 = {$31.034 * (4 * 200)} – ($100 * 200)

                                  = $24,827.20 - $20,000

                                  = $4,827.20

Hence, the total benefit to the shareholders of the B is $4,827.20.

4.

The formula to calculate the share price of the company after merger in case of cash takeover is as follows:

MPSA+B = {(MPS of A * Number of shares outstanding of A) + (MPS of B * Number of shares outstanding of B) + Synergy} / Number of shares outstanding of A

            = {($30 * 5,000) + ($100 * 200) + $10,000} / 5,000

            = $180,000 / 5,000

            = $36

Hence, the share price of the company after merger is $36.